# Precalculus Algebra

**I. MTH 112 Precalculus Algebra - 3 Semester Hours
Core Area III, TMTH**

**II. Course Description**

This course emphasizes the algebra of functions –
including polynomial, rational,

exponential, and logarithmic functions. The course also covers systems of
equations and

inequalities, quadratic inequalities, and the binomial theorem. Additional
topics may

include matrices, Cramer’ s Rule , and mathematical induction .

**III. Prerequisite**

A minimum prerequisite of high school Algebra I, Geometry,
and Algebra II with an

appropriate mathematics placement score. An alternative to this is that the
student should

successfully pass with a C or higher in Intermediate College Algebra.

**IV. Textbook**

__Precalculus: Mathematics for Calculus,__ Stewart,
Redlin, Watson 5^th Ed.

Thomson/Brooks/Cole, 2006.

**V. Course Objectives**

The objective of this course is to provide an
understanding of concepts, develop

competent skills, and demonstrate applications in the following areas:

1. analytic and geometric interpretation of algebraic,
exponential, and logarithmic

functions

2. analytic and geometric interpretation of systems of equations and
inequalities

While building on the manipulative skills from algebra this course strives to

develop analytic skills as a preparation for further mathematical applications
or

courses in mathematics requiring knowledge of algebraic and transcendental

functions.

**VI. Course Outline of Topics**

A. This course shall include the following topics as a minimum.

1. Cartesion plane

2 Graphs of equations

3. Lines in the plane

4. Functions

5. Graphs of functions

6. Combinations of functions

7. Inverse functions

8. Variation

9. Quadratic functions

10. Higher degree functions

11. Real zeros

12. Complex numbers

13. Fundamental Theorem of algebra

14. Rational functions

15. Partial fractions

16. Exponential functions

17. Logarithmic functions

18. Properties of logarithms

19. Solving exponential and logarithmic equations

20. Applications

21. Systems of equations

22. Systems in two variables

23. Systems of more than two variables

24. Systems of inequalities

25. Linear programming

26. Quadratic inequalities

27. Binomial Theorem

B. Optional topics may include the following

1. Matrices and systems of equations

2. Operations with matrices

3. Inverse matrices

4. Determinant of a matrix

5. Properties of determinants

6. Applications

7. Sequences, summation notation

8. Arithmetic sequence

9. Geometric sequence

10. Mathematical induction

**VII. Evaluation and Assessment**

A. College requirements:

Examinations should be given by instructors periodically throughout their
courses.

Faculty are encouraged to give evaluative work early in the term so that
students will

have a clear understanding of the progress they are making. Final examinations
will be

given in all classes, and all students enrolled for academic credit will take
the final

examination. (College Handbook, section 3.7)

B. Grading system as stated in the college catalog:

*A - Excellent (90-100%)

*B - Good (80-89%)

*C - Average (70-79%)

D – Poor (60-69%)

F – Failure (below 60%)

W - Withdrawal (before midterm)

WP - Withdrawal passing (after midterm)

WF - Withdrawal failure (after midterm)

I - Incomplete

AU - Audit

RW - Required withdrawal

*Satisfactory grades

C. Evaluation and assessment techniques may include any or all of the following:

1. Recitation

2. Daily assignments

3. Written assignments

4. Computer assignments

5. Projects

6. Participation

7. Exams

To receive a grade of “C” or higher, the student must
obtain an average of at least

70% on written test(s) and other evaluation criteria as determined by the
instructor.

**** Note: A grade of "C" or higher is required in this
course for a student to be
eligible for MTH 113 or MTH 120.**

**VIII. Class Activities**

A. Lecture.

B. Recitation.

C. Discussion.

D. Individual instruction.

E. Testing.

**IX. GENERAL COURSE COMPETENCIES**

A. The student will acquire knowledge of mathematical
terminology.

B. The student will acquire knowledge of inequalities.

C. The student will acquire knowledge of functions and their graphs.

D. The student will be able to use concepts of precalculus algebra in problem

solving.

**X. COURSE OBJECTIVES STATED IN PERFORMANCE TERMS**

A. The student will demonstrate knowledge of mathematical
terminology as

measured by his/her ability to recall the meaning of the following in order to

work problems requiring knowledge of these terms:

1. transformations

2. point-slope form

3. domain

4. range

5. function

6. vertex

7. composite function

8. one-to-one function

9. inverse function

10. polynomial function

11. exponential function

12. logarithmic function

13. base e

14. rational function

15. local extrema

16. roots (zeros)

17. synthetic division

18. asymptotes

19. binomial theorem

20. Fundamental Theorem of Algebra

21. factor Theorem

22. remainder Theorem

23. complex number

B. The student will demonstrate knowledge of inequalities
by his/her

ability to

1. express given inequalities in interval notation.

2. solve polynomial and rational inequalities.

3. solve inequalities involving absolute value .

4. solve systems of inequalities.

C. The student will demonstrate knowledge of functions and
their graphs by

his/her ability to

1. find the domain and range of a function.

2. find the composition of functions.

3. find the inverse of a given function.

4. solve equations involving different kinds of functions, including

the following:

a. linear

b. quadratic

c. polynomial

d. rational

e. exponential

g. absolute value

f. logarithmic

5. write the equation of a linear function in point/slope form.

6. use synthetic division to

a. evaluate polynomials.

b. factor polynomials.

c. find real and complex zeros of a polynomial function.

7. draw graphs of different kinds of functions including the

following:

a. linear

b. quadratic

c. polynomial

d. rational

e. exponential

f. logarithmic

g. absolute value

h. piecewise

i. radical

8. graph functions using transformations.

9. draw the inverse graph of a function given the graph of the

function.

10.use properties of logarithms/exponents to solve given problems.

D. The student will demonstrate his/her ability to use the following concepts of

precalculus algebra to solve applied problems:

1. quadratic functions.

2. exponential functions.

3. logarithmic functions.

4. other function types studied.

5. nonlinear systems of equations.

**XI. Attendance**

Students are expected to attend all classes for which they
are registered. Students who are

unable to attend class regularly, regardless of the reason or circumstance,
should

withdraw from that class before poor attendance interferes with the student’s
ability to

achieve the objectives required in the course. Withdrawal from class can affect
eligibility

for federal financial aid.

**XII. Statement on Discrimination/Harassment**

The College and the Alabama State Board of Education are
committed to providing both

employment and educational environments free of harassment or discrimination
related to

an individual’s race, color, gender, religion, national origin, age, or
disability. Such

harassment is a violation of State Board of Education policy. Any practice or
behavior

that constitutes harassment or discrimination will not be tolerated.

**XIII. Americans with Disabilities**

The Rehabilitation Act of 1973 (Section 504) and the
Americans with Disabilities Act of

1990 state that qualified students with disabilities who meet the essential
functions and

academic requirements are entitled to reasonable accommodations. It is the
student’s

responsibility to provide appropriate disability documentation to the College.
The ADA

Accommodations office is located in FSC 300 (205-856-7731).

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